Since the invention of the laser and the definition of its transverse modes, many studies have considered the question of a beam quality factor for arbitrary laser modes. In the early 1990s tools traditionally associated with statistics were applied to laser beams with uniform single mode and separable polarisation (scalar beams), exploiting the analogous behaviour between probability density functions and laser beam intensity profiles. Viewing the latter as a probability of finding the light, statistical moments were used to define beam and divergence widths as second moments of the intensity, ultimately giving rise to a beam quality factor, M2, as a single measure of any scalar mode. This measure has since been extensively studied, with corresponding digital measurement techniques, and is incorporated into the ISO standards for measuring and defining laser beams.
In recent years, laser beams with non-uniform polarisation distributions having non-separable, multi-directional polarisation, so called vector beams, have become topical due to the scope of their applications in topics as diverse as optical microscopy, optical tweezers, quantum memories, and data encryption to mention but a few. Over the past few years, a variety of means to generate vector vortex beams have being envisioned, internal and external to laser cavities in either interferometric, or direct ways.
Despite the many advances in generating them, the means to detect or analyse them lags behind. Such detection techniques include the use of rotating analysers together with interferometers, as well as geometric phase plates with single-mode fibres. Importantly, no quantitative measure exists to define the quality of a vector mode: i.e., to differentiate them from scalar modes. Presently this is done by qualitative means, e.g., measuring the profile change after a polariser, or by averaging the degree of polarisation across the beam.
What is required are standards which can be used for such vector beams, and the present invention proposes such a measure which could be developed into an international standard. It is therefore an object of this present invention to address the aforementioned requirement and provide a quantitative beam quality measure for vector beams.